In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-module M is called strongly Gorenstein flat if there is an exact sequence · · · → P 1 → P 0 → P 0 → P 1 → · · · of projective R-modules with M = ker(P 0 → P 1 ) such that Hom(−, F) leaves the sequence exact whenever F is a flat R-module. Several well-known classes of rings are characterized in terms of strongly Gorenstein flat modules. Some examples are given to show that strongly Gorenstein flat modules over coherent rings lie strictly between projective modules and Gorenstein flat modules. The strongly Gorenstein flat dimension and the existence of strongly Gorenstein flat precovers and pre-envelopes are also studied.2000 Mathematics subject classification: primary 16D40; secondary 16E05, 18G20.

Let G be a finite cyclic group. Every sequence S over G can be written in the form S = (n1g) · . . . · (n l g) where g ∈ G and n1, . . . , n l ∈ [1, ord(g)], and the index ind(S) of S is defined to be the minimum of (n1 + · · · + n l )/ ord(g) over all possible g ∈ G such that g = G. An open problem on the index of length four sequences asks whether or not every minimal zero-sum sequence of length 4 over a finite cyclic group G with gcd(|G|, 6) = 1 has index 1. In this paper, we show that if G = g is a cyclic group with order of a product of two prime powers and gcd(|G|, 6) = 1, then every minimal zero-sum sequence S of the form S = (g)(n2g)(n3g)(n4g) has index 1. In particular, our result confirms that the above problem has an affirmative answer when the order of G is a product of two different prime numbers or a prime power, extending a recent result by the first author, Plyley, Yuan and Zeng.2000 Mathematics Subject Classification. Primary 11B30 11B50 20K01.

BackgroundSeveral angiostrongyliasis outbreaks have been reported in recent years but the disease continues to be neglected in public health circles. We describe an outbreak in Dali, southwest China in order to highlight some key problems for the control of this helminth infection.Methodology/Principal FindingsAll available medical records of suspected angiostrongyliasis patients visiting hospitals in Dali in the period 1 October 2007–31 March 2008 were reviewed, and tentative diagnoses of varying strengths were reached according to given sets of criteria. Snails collected from local markets, restaurants and natural habitats were also screened for the presence of Angiostrongylus cantonensis. A total of 33 patients met criteria for infection, and 11 among them were classified as clinically confirmed. An additional eight patients were identified through a surveillance system put in operation in response to the outbreak. The epidemic lasted for 8 months with its peak in February 2008. Of the 33 patients, 97.0% complained of severe headache. 84.8% patients had high eosinophil cell counts either in the peripheral blood or in cerebrospinal fluid (CSF). Three-quarters of the patients were treated with a combination of albendazole and corticosteroids, resulting in significantly improved overall conditions. Twenty-two patients reported the consumption of raw or undercooked snails prior to the onset of the symptoms, and approximately 1.0% of the Pomacea canaliculata snails on sale were found to be infected with A. cantonensis. The snails were also found in certain habitats around Dali but no parasites were detected in these populations.Conclusions/SignificanceThe import and sale of infected P. canaliculata is the likely trigger for this angiostrongyliasis outbreak. Awareness of angiostrongyliasis must be raised, and standardized diagnosis and treatment are needed in order to provide clinicians with a guide to address this disease. Health education campaigns could limit the risk, and a hospital-based surveillance system should be established in order to detect future outbreaks.

such as global warming and climate changes. [1][2][3][4] Solar energy is clean and abundant, for example, nearly four million exajoules (4 × 10 18 J) of solar energy reaches the earth annually. [1,5] Conversion of solar energy into chemical energy through photocatalytic decomposition of water to produce hydrogen is one of the suitable approaches to utilize solar energy. [6][7][8][9][10] The different types of fundamental photocatalytic reactions include i) semiconductor-based photocatalysis, ii) dye-sensitized semiconductor-based photo catalysis, iii) quantum dot-based photocatalysis, iv) 2D layered materials-based photocatalysts, and v) plasmonic photocatalysts. [11] Photocatalytic hydrogen evolution reaction (HER) are mainly based on inorganic semiconductor and poly merbased organic semiconductors, for exampl, in a conventional dye-sensitized semiconductor photocatalytic hydrogen production system, the dye molecules are excited to inject electrons into the conduction band of a semiconductor or polymer (inorganic semiconductor TiO 2 or g-C 3 N 4 is usually chosen), then the electrons are quickly captured by the co-catalyst (such as precious metals Efficient photocatalytic hydrogen evolution reaction (HER) in the visibleto-near infrared region at a low cost remains a challenging issue. This work demonstrates the fabrication of organic-inorganic composites by deposition of supramolecular aggregates of a chlorophyll derivative, namely, zinc methyl 3-devinyl-3-hydroxymethyl-pyropheophorbide a (Chl) on the surface of Ti 3 C 2 T x MXene with 2D accordion-like morphology. This composite material isemployed as noble metal-free catalyst in photocatalytic HER under the white light illumination, where Chl serves as a small molecule organic semiconductor component instead of ordinary inorganic and polymer organic semiconductors such as TiO 2 and g-C 3 N 4 , and Ti 3 C 2 T x serves as a co-catalyst. Different composition ratios of Chl/Ti 3 C 2 T x are compared for their light-harvesting ability, morphology, charge transfer efficiency, and photocatalytic performance. The best HER performance is found to be as high as 52 ± 5 µmol h −1 g cat −1 after optimization. Such a large HER activity is attributed to the efficient light harvesting followed by exciton transfer in Chl aggregates and the resultant charge separation at the interface of Chl/Ti 3 C 2 T x .

An element of a ring R with identity is called strongly clean if it is the sum of an idempotent and a unit that commute, and R is called strongly clean if every element of R is strongly clean. In this paper, we determine when a 2 × 2 matrix A over a commutative local ring is strongly clean. Several equivalent criteria are given for such a matrix to be strongly clean. Consequently, we obtain several equivalent conditions for the 2 × 2 matrix ring over a commutative local ring to be strongly clean, extending a result of Chen, Yang, and Zhou.